Chapter_03
Pankaj Kumar
12/23/2017
Load MASS library, as we need to work on Boston dataset.
library(MASS)
#Boston
names(Boston)## [1] "crim" "zn" "indus" "chas" "nox" "rm" "age"
## [8] "dis" "rad" "tax" "ptratio" "black" "lstat" "medv"We will create a simple single linear regression model with Boston library’s lstat as predictor and medv as response.
#lm.fit=lm(medv~lstat, data=Boston)
attach(Boston)
lm.fit = lm(medv~lstat)
lm.fit##
## Call:
## lm(formula = medv ~ lstat)
##
## Coefficients:
## (Intercept) lstat
## 34.55 -0.95summary(lm.fit)##
## Call:
## lm(formula = medv ~ lstat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.168 -3.990 -1.318 2.034 24.500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 34.55384 0.56263 61.41 <2e-16 ***
## lstat -0.95005 0.03873 -24.53 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.216 on 504 degrees of freedom
## Multiple R-squared: 0.5441, Adjusted R-squared: 0.5432
## F-statistic: 601.6 on 1 and 504 DF, p-value: < 2.2e-16anova(lm.fit)## Analysis of Variance Table
##
## Response: medv
## Df Sum Sq Mean Sq F value Pr(>F)
## lstat 1 23244 23243.9 601.62 < 2.2e-16 ***
## Residuals 504 19472 38.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot(lstat, medv)
abline(h=mean(medv))
abline(lm.fit, col="blue")
names(lm.fit)## [1] "coefficients" "residuals" "effects" "rank"
## [5] "fitted.values" "assign" "qr" "df.residual"
## [9] "xlevels" "call" "terms" "model"confint(lm.fit)## 2.5 % 97.5 %
## (Intercept) 33.448457 35.6592247
## lstat -1.026148 -0.8739505predict(lm.fit ,data.frame(lstat=c(5 ,10 ,15)),interval ="confidence")## fit lwr upr
## 1 29.80359 29.00741 30.59978
## 2 25.05335 24.47413 25.63256
## 3 20.30310 19.73159 20.87461Residual plots:
plot(lm.fit)
Now that we have gone through a single linear regression model (with one predictor), we will create a multiple linear regression model with all thirteen predictors:
mul.lm.fit = lm(medv ~ ., data = Boston)
summary(mul.lm.fit)##
## Call:
## lm(formula = medv ~ ., data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.595 -2.730 -0.518 1.777 26.199
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.646e+01 5.103e+00 7.144 3.28e-12 ***
## crim -1.080e-01 3.286e-02 -3.287 0.001087 **
## zn 4.642e-02 1.373e-02 3.382 0.000778 ***
## indus 2.056e-02 6.150e-02 0.334 0.738288
## chas 2.687e+00 8.616e-01 3.118 0.001925 **
## nox -1.777e+01 3.820e+00 -4.651 4.25e-06 ***
## rm 3.810e+00 4.179e-01 9.116 < 2e-16 ***
## age 6.922e-04 1.321e-02 0.052 0.958229
## dis -1.476e+00 1.995e-01 -7.398 6.01e-13 ***
## rad 3.060e-01 6.635e-02 4.613 5.07e-06 ***
## tax -1.233e-02 3.760e-03 -3.280 0.001112 **
## ptratio -9.527e-01 1.308e-01 -7.283 1.31e-12 ***
## black 9.312e-03 2.686e-03 3.467 0.000573 ***
## lstat -5.248e-01 5.072e-02 -10.347 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.745 on 492 degrees of freedom
## Multiple R-squared: 0.7406, Adjusted R-squared: 0.7338
## F-statistic: 108.1 on 13 and 492 DF, p-value: < 2.2e-16plot(mul.lm.fit)
Multiple linear regression without a predictor, for example: age.
mul.lm.fit.without.age = update(mul.lm.fit, ~ . -age)
summary(mul.lm.fit.without.age)##
## Call:
## lm(formula = medv ~ crim + zn + indus + chas + nox + rm + dis +
## rad + tax + ptratio + black + lstat, data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.6054 -2.7313 -0.5188 1.7601 26.2243
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36.436927 5.080119 7.172 2.72e-12 ***
## crim -0.108006 0.032832 -3.290 0.001075 **
## zn 0.046334 0.013613 3.404 0.000719 ***
## indus 0.020562 0.061433 0.335 0.737989
## chas 2.689026 0.859598 3.128 0.001863 **
## nox -17.713540 3.679308 -4.814 1.97e-06 ***
## rm 3.814394 0.408480 9.338 < 2e-16 ***
## dis -1.478612 0.190611 -7.757 5.03e-14 ***
## rad 0.305786 0.066089 4.627 4.75e-06 ***
## tax -0.012329 0.003755 -3.283 0.001099 **
## ptratio -0.952211 0.130294 -7.308 1.10e-12 ***
## black 0.009321 0.002678 3.481 0.000544 ***
## lstat -0.523852 0.047625 -10.999 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.74 on 493 degrees of freedom
## Multiple R-squared: 0.7406, Adjusted R-squared: 0.7343
## F-statistic: 117.3 on 12 and 493 DF, p-value: < 2.2e-16Multiple linear regression with interaction terms
mul.lm.fit.interact.age = lm(medv ~ lstat * age, data = Boston)
summary(mul.lm.fit.interact.age)##
## Call:
## lm(formula = medv ~ lstat * age, data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.806 -4.045 -1.333 2.085 27.552
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36.0885359 1.4698355 24.553 < 2e-16 ***
## lstat -1.3921168 0.1674555 -8.313 8.78e-16 ***
## age -0.0007209 0.0198792 -0.036 0.9711
## lstat:age 0.0041560 0.0018518 2.244 0.0252 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.149 on 502 degrees of freedom
## Multiple R-squared: 0.5557, Adjusted R-squared: 0.5531
## F-statistic: 209.3 on 3 and 502 DF, p-value: < 2.2e-16Non-linear Transformations of the Predictors with single predictor:
lm.fit.non.linear = lm(medv ~ lstat + I(lstat^2), data = Boston)
summary(lm.fit.non.linear)##
## Call:
## lm(formula = medv ~ lstat + I(lstat^2), data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.2834 -3.8313 -0.5295 2.3095 25.4148
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 42.862007 0.872084 49.15 <2e-16 ***
## lstat -2.332821 0.123803 -18.84 <2e-16 ***
## I(lstat^2) 0.043547 0.003745 11.63 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.524 on 503 degrees of freedom
## Multiple R-squared: 0.6407, Adjusted R-squared: 0.6393
## F-statistic: 448.5 on 2 and 503 DF, p-value: < 2.2e-16plot(lm.fit.non.linear)
# attach(Boston)
# plot(lstat, medv)
# abline(lm.fit.non.linear, col="blue")
anova(lm.fit, lm.fit.non.linear)## Analysis of Variance Table
##
## Model 1: medv ~ lstat
## Model 2: medv ~ lstat + I(lstat^2)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 504 19472
## 2 503 15347 1 4125.1 135.2 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Polynomial fit for linear regression:
lm.fit.non.linear.degree5 = lm(medv ~ poly(lstat, 5), data = Boston)
summary(lm.fit.non.linear.degree5)##
## Call:
## lm(formula = medv ~ poly(lstat, 5), data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.5433 -3.1039 -0.7052 2.0844 27.1153
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.5328 0.2318 97.197 < 2e-16 ***
## poly(lstat, 5)1 -152.4595 5.2148 -29.236 < 2e-16 ***
## poly(lstat, 5)2 64.2272 5.2148 12.316 < 2e-16 ***
## poly(lstat, 5)3 -27.0511 5.2148 -5.187 3.10e-07 ***
## poly(lstat, 5)4 25.4517 5.2148 4.881 1.42e-06 ***
## poly(lstat, 5)5 -19.2524 5.2148 -3.692 0.000247 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.215 on 500 degrees of freedom
## Multiple R-squared: 0.6817, Adjusted R-squared: 0.6785
## F-statistic: 214.2 on 5 and 500 DF, p-value: < 2.2e-16plot(lm.fit.non.linear.degree5)
======================CARSEATS DATASET FOR QUALITATIVE PREDICTORS========================
library(ISLR)
names(Carseats)## [1] "Sales" "CompPrice" "Income" "Advertising" "Population"
## [6] "Price" "ShelveLoc" "Age" "Education" "Urban"
## [11] "US"Carseats## Sales CompPrice Income Advertising Population Price ShelveLoc Age
## 1 9.50 138 73 11 276 120 Bad 42
## 2 11.22 111 48 16 260 83 Good 65
## 3 10.06 113 35 10 269 80 Medium 59
## 4 7.40 117 100 4 466 97 Medium 55
## 5 4.15 141 64 3 340 128 Bad 38
## 6 10.81 124 113 13 501 72 Bad 78
## 7 6.63 115 105 0 45 108 Medium 71
## 8 11.85 136 81 15 425 120 Good 67
## 9 6.54 132 110 0 108 124 Medium 76
## 10 4.69 132 113 0 131 124 Medium 76
## 11 9.01 121 78 9 150 100 Bad 26
## 12 11.96 117 94 4 503 94 Good 50
## 13 3.98 122 35 2 393 136 Medium 62
## 14 10.96 115 28 11 29 86 Good 53
## 15 11.17 107 117 11 148 118 Good 52
## 16 8.71 149 95 5 400 144 Medium 76
## 17 7.58 118 32 0 284 110 Good 63
## 18 12.29 147 74 13 251 131 Good 52
## 19 13.91 110 110 0 408 68 Good 46
## 20 8.73 129 76 16 58 121 Medium 69
## 21 6.41 125 90 2 367 131 Medium 35
## 22 12.13 134 29 12 239 109 Good 62
## 23 5.08 128 46 6 497 138 Medium 42
## 24 5.87 121 31 0 292 109 Medium 79
## 25 10.14 145 119 16 294 113 Bad 42
## 26 14.90 139 32 0 176 82 Good 54
## 27 8.33 107 115 11 496 131 Good 50
## 28 5.27 98 118 0 19 107 Medium 64
## 29 2.99 103 74 0 359 97 Bad 55
## 30 7.81 104 99 15 226 102 Bad 58
## 31 13.55 125 94 0 447 89 Good 30
## 32 8.25 136 58 16 241 131 Medium 44
## 33 6.20 107 32 12 236 137 Good 64
## 34 8.77 114 38 13 317 128 Good 50
## 35 2.67 115 54 0 406 128 Medium 42
## 36 11.07 131 84 11 29 96 Medium 44
## 37 8.89 122 76 0 270 100 Good 60
## 38 4.95 121 41 5 412 110 Medium 54
## 39 6.59 109 73 0 454 102 Medium 65
## 40 3.24 130 60 0 144 138 Bad 38
## 41 2.07 119 98 0 18 126 Bad 73
## 42 7.96 157 53 0 403 124 Bad 58
## 43 10.43 77 69 0 25 24 Medium 50
## 44 4.12 123 42 11 16 134 Medium 59
## 45 4.16 85 79 6 325 95 Medium 69
## 46 4.56 141 63 0 168 135 Bad 44
## 47 12.44 127 90 14 16 70 Medium 48
## 48 4.38 126 98 0 173 108 Bad 55
## 49 3.91 116 52 0 349 98 Bad 69
## 50 10.61 157 93 0 51 149 Good 32
## 51 1.42 99 32 18 341 108 Bad 80
## 52 4.42 121 90 0 150 108 Bad 75
## 53 7.91 153 40 3 112 129 Bad 39
## 54 6.92 109 64 13 39 119 Medium 61
## 55 4.90 134 103 13 25 144 Medium 76
## 56 6.85 143 81 5 60 154 Medium 61
## 57 11.91 133 82 0 54 84 Medium 50
## 58 0.91 93 91 0 22 117 Bad 75
## 59 5.42 103 93 15 188 103 Bad 74
## 60 5.21 118 71 4 148 114 Medium 80
## 61 8.32 122 102 19 469 123 Bad 29
## 62 7.32 105 32 0 358 107 Medium 26
## 63 1.82 139 45 0 146 133 Bad 77
## 64 8.47 119 88 10 170 101 Medium 61
## 65 7.80 100 67 12 184 104 Medium 32
## 66 4.90 122 26 0 197 128 Medium 55
## 67 8.85 127 92 0 508 91 Medium 56
## 68 9.01 126 61 14 152 115 Medium 47
## 69 13.39 149 69 20 366 134 Good 60
## 70 7.99 127 59 0 339 99 Medium 65
## 71 9.46 89 81 15 237 99 Good 74
## 72 6.50 148 51 16 148 150 Medium 58
## 73 5.52 115 45 0 432 116 Medium 25
## 74 12.61 118 90 10 54 104 Good 31
## 75 6.20 150 68 5 125 136 Medium 64
## 76 8.55 88 111 23 480 92 Bad 36
## 77 10.64 102 87 10 346 70 Medium 64
## 78 7.70 118 71 12 44 89 Medium 67
## 79 4.43 134 48 1 139 145 Medium 65
## 80 9.14 134 67 0 286 90 Bad 41
## 81 8.01 113 100 16 353 79 Bad 68
## 82 7.52 116 72 0 237 128 Good 70
## 83 11.62 151 83 4 325 139 Good 28
## 84 4.42 109 36 7 468 94 Bad 56
## 85 2.23 111 25 0 52 121 Bad 43
## 86 8.47 125 103 0 304 112 Medium 49
## 87 8.70 150 84 9 432 134 Medium 64
## 88 11.70 131 67 7 272 126 Good 54
## 89 6.56 117 42 7 144 111 Medium 62
## 90 7.95 128 66 3 493 119 Medium 45
## 91 5.33 115 22 0 491 103 Medium 64
## 92 4.81 97 46 11 267 107 Medium 80
## 93 4.53 114 113 0 97 125 Medium 29
## 94 8.86 145 30 0 67 104 Medium 55
## 95 8.39 115 97 5 134 84 Bad 55
## 96 5.58 134 25 10 237 148 Medium 59
## 97 9.48 147 42 10 407 132 Good 73
## 98 7.45 161 82 5 287 129 Bad 33
## 99 12.49 122 77 24 382 127 Good 36
## 100 4.88 121 47 3 220 107 Bad 56
## 101 4.11 113 69 11 94 106 Medium 76
## 102 6.20 128 93 0 89 118 Medium 34
## 103 5.30 113 22 0 57 97 Medium 65
## 104 5.07 123 91 0 334 96 Bad 78
## 105 4.62 121 96 0 472 138 Medium 51
## 106 5.55 104 100 8 398 97 Medium 61
## 107 0.16 102 33 0 217 139 Medium 70
## 108 8.55 134 107 0 104 108 Medium 60
## 109 3.47 107 79 2 488 103 Bad 65
## 110 8.98 115 65 0 217 90 Medium 60
## 111 9.00 128 62 7 125 116 Medium 43
## 112 6.62 132 118 12 272 151 Medium 43
## 113 6.67 116 99 5 298 125 Good 62
## 114 6.01 131 29 11 335 127 Bad 33
## 115 9.31 122 87 9 17 106 Medium 65
## 116 8.54 139 35 0 95 129 Medium 42
## 117 5.08 135 75 0 202 128 Medium 80
## 118 8.80 145 53 0 507 119 Medium 41
## 119 7.57 112 88 2 243 99 Medium 62
## 120 7.37 130 94 8 137 128 Medium 64
## 121 6.87 128 105 11 249 131 Medium 63
## 122 11.67 125 89 10 380 87 Bad 28
## 123 6.88 119 100 5 45 108 Medium 75
## 124 8.19 127 103 0 125 155 Good 29
## 125 8.87 131 113 0 181 120 Good 63
## 126 9.34 89 78 0 181 49 Medium 43
## 127 11.27 153 68 2 60 133 Good 59
## 128 6.52 125 48 3 192 116 Medium 51
## 129 4.96 133 100 3 350 126 Bad 55
## 130 4.47 143 120 7 279 147 Bad 40
## 131 8.41 94 84 13 497 77 Medium 51
## 132 6.50 108 69 3 208 94 Medium 77
## 133 9.54 125 87 9 232 136 Good 72
## 134 7.62 132 98 2 265 97 Bad 62
## 135 3.67 132 31 0 327 131 Medium 76
## 136 6.44 96 94 14 384 120 Medium 36
## 137 5.17 131 75 0 10 120 Bad 31
## 138 6.52 128 42 0 436 118 Medium 80
## 139 10.27 125 103 12 371 109 Medium 44
## 140 12.30 146 62 10 310 94 Medium 30
## 141 6.03 133 60 10 277 129 Medium 45
## 142 6.53 140 42 0 331 131 Bad 28
## 143 7.44 124 84 0 300 104 Medium 77
## 144 0.53 122 88 7 36 159 Bad 28
## 145 9.09 132 68 0 264 123 Good 34
## 146 8.77 144 63 11 27 117 Medium 47
## 147 3.90 114 83 0 412 131 Bad 39
## 148 10.51 140 54 9 402 119 Good 41
## 149 7.56 110 119 0 384 97 Medium 72
## 150 11.48 121 120 13 140 87 Medium 56
## 151 10.49 122 84 8 176 114 Good 57
## 152 10.77 111 58 17 407 103 Good 75
## 153 7.64 128 78 0 341 128 Good 45
## 154 5.93 150 36 7 488 150 Medium 25
## 155 6.89 129 69 10 289 110 Medium 50
## 156 7.71 98 72 0 59 69 Medium 65
## 157 7.49 146 34 0 220 157 Good 51
## 158 10.21 121 58 8 249 90 Medium 48
## 159 12.53 142 90 1 189 112 Good 39
## 160 9.32 119 60 0 372 70 Bad 30
## 161 4.67 111 28 0 486 111 Medium 29
## 162 2.93 143 21 5 81 160 Medium 67
## 163 3.63 122 74 0 424 149 Medium 51
## 164 5.68 130 64 0 40 106 Bad 39
## 165 8.22 148 64 0 58 141 Medium 27
## 166 0.37 147 58 7 100 191 Bad 27
## 167 6.71 119 67 17 151 137 Medium 55
## 168 6.71 106 73 0 216 93 Medium 60
## 169 7.30 129 89 0 425 117 Medium 45
## 170 11.48 104 41 15 492 77 Good 73
## 171 8.01 128 39 12 356 118 Medium 71
## 172 12.49 93 106 12 416 55 Medium 75
## 173 9.03 104 102 13 123 110 Good 35
## 174 6.38 135 91 5 207 128 Medium 66
## 175 0.00 139 24 0 358 185 Medium 79
## 176 7.54 115 89 0 38 122 Medium 25
## 177 5.61 138 107 9 480 154 Medium 47
## 178 10.48 138 72 0 148 94 Medium 27
## 179 10.66 104 71 14 89 81 Medium 25
## 180 7.78 144 25 3 70 116 Medium 77
## 181 4.94 137 112 15 434 149 Bad 66
## 182 7.43 121 83 0 79 91 Medium 68
## 183 4.74 137 60 4 230 140 Bad 25
## 184 5.32 118 74 6 426 102 Medium 80
## 185 9.95 132 33 7 35 97 Medium 60
## 186 10.07 130 100 11 449 107 Medium 64
## 187 8.68 120 51 0 93 86 Medium 46
## 188 6.03 117 32 0 142 96 Bad 62
## 189 8.07 116 37 0 426 90 Medium 76
## 190 12.11 118 117 18 509 104 Medium 26
## 191 8.79 130 37 13 297 101 Medium 37
## 192 6.67 156 42 13 170 173 Good 74
## 193 7.56 108 26 0 408 93 Medium 56
## 194 13.28 139 70 7 71 96 Good 61
## 195 7.23 112 98 18 481 128 Medium 45
## 196 4.19 117 93 4 420 112 Bad 66
## 197 4.10 130 28 6 410 133 Bad 72
## 198 2.52 124 61 0 333 138 Medium 76
## 199 3.62 112 80 5 500 128 Medium 69
## 200 6.42 122 88 5 335 126 Medium 64
## 201 5.56 144 92 0 349 146 Medium 62
## 202 5.94 138 83 0 139 134 Medium 54
## 203 4.10 121 78 4 413 130 Bad 46
## 204 2.05 131 82 0 132 157 Bad 25
## 205 8.74 155 80 0 237 124 Medium 37
## 206 5.68 113 22 1 317 132 Medium 28
## 207 4.97 162 67 0 27 160 Medium 77
## 208 8.19 111 105 0 466 97 Bad 61
## 209 7.78 86 54 0 497 64 Bad 33
## 210 3.02 98 21 11 326 90 Bad 76
## 211 4.36 125 41 2 357 123 Bad 47
## 212 9.39 117 118 14 445 120 Medium 32
## 213 12.04 145 69 19 501 105 Medium 45
## 214 8.23 149 84 5 220 139 Medium 33
## 215 4.83 115 115 3 48 107 Medium 73
## 216 2.34 116 83 15 170 144 Bad 71
## 217 5.73 141 33 0 243 144 Medium 34
## 218 4.34 106 44 0 481 111 Medium 70
## 219 9.70 138 61 12 156 120 Medium 25
## 220 10.62 116 79 19 359 116 Good 58
## 221 10.59 131 120 15 262 124 Medium 30
## 222 6.43 124 44 0 125 107 Medium 80
## 223 7.49 136 119 6 178 145 Medium 35
## 224 3.45 110 45 9 276 125 Medium 62
## 225 4.10 134 82 0 464 141 Medium 48
## 226 6.68 107 25 0 412 82 Bad 36
## 227 7.80 119 33 0 245 122 Good 56
## 228 8.69 113 64 10 68 101 Medium 57
## 229 5.40 149 73 13 381 163 Bad 26
## 230 11.19 98 104 0 404 72 Medium 27
## 231 5.16 115 60 0 119 114 Bad 38
## 232 8.09 132 69 0 123 122 Medium 27
## 233 13.14 137 80 10 24 105 Good 61
## 234 8.65 123 76 18 218 120 Medium 29
## 235 9.43 115 62 11 289 129 Good 56
## 236 5.53 126 32 8 95 132 Medium 50
## 237 9.32 141 34 16 361 108 Medium 69
## 238 9.62 151 28 8 499 135 Medium 48
## 239 7.36 121 24 0 200 133 Good 73
## 240 3.89 123 105 0 149 118 Bad 62
## 241 10.31 159 80 0 362 121 Medium 26
## 242 12.01 136 63 0 160 94 Medium 38
## 243 4.68 124 46 0 199 135 Medium 52
## 244 7.82 124 25 13 87 110 Medium 57
## 245 8.78 130 30 0 391 100 Medium 26
## 246 10.00 114 43 0 199 88 Good 57
## 247 6.90 120 56 20 266 90 Bad 78
## 248 5.04 123 114 0 298 151 Bad 34
## 249 5.36 111 52 0 12 101 Medium 61
## 250 5.05 125 67 0 86 117 Bad 65
## 251 9.16 137 105 10 435 156 Good 72
## 252 3.72 139 111 5 310 132 Bad 62
## 253 8.31 133 97 0 70 117 Medium 32
## 254 5.64 124 24 5 288 122 Medium 57
## 255 9.58 108 104 23 353 129 Good 37
## 256 7.71 123 81 8 198 81 Bad 80
## 257 4.20 147 40 0 277 144 Medium 73
## 258 8.67 125 62 14 477 112 Medium 80
## 259 3.47 108 38 0 251 81 Bad 72
## 260 5.12 123 36 10 467 100 Bad 74
## 261 7.67 129 117 8 400 101 Bad 36
## 262 5.71 121 42 4 188 118 Medium 54
## 263 6.37 120 77 15 86 132 Medium 48
## 264 7.77 116 26 6 434 115 Medium 25
## 265 6.95 128 29 5 324 159 Good 31
## 266 5.31 130 35 10 402 129 Bad 39
## 267 9.10 128 93 12 343 112 Good 73
## 268 5.83 134 82 7 473 112 Bad 51
## 269 6.53 123 57 0 66 105 Medium 39
## 270 5.01 159 69 0 438 166 Medium 46
## 271 11.99 119 26 0 284 89 Good 26
## 272 4.55 111 56 0 504 110 Medium 62
## 273 12.98 113 33 0 14 63 Good 38
## 274 10.04 116 106 8 244 86 Medium 58
## 275 7.22 135 93 2 67 119 Medium 34
## 276 6.67 107 119 11 210 132 Medium 53
## 277 6.93 135 69 14 296 130 Medium 73
## 278 7.80 136 48 12 326 125 Medium 36
## 279 7.22 114 113 2 129 151 Good 40
## 280 3.42 141 57 13 376 158 Medium 64
## 281 2.86 121 86 10 496 145 Bad 51
## 282 11.19 122 69 7 303 105 Good 45
## 283 7.74 150 96 0 80 154 Good 61
## 284 5.36 135 110 0 112 117 Medium 80
## 285 6.97 106 46 11 414 96 Bad 79
## 286 7.60 146 26 11 261 131 Medium 39
## 287 7.53 117 118 11 429 113 Medium 67
## 288 6.88 95 44 4 208 72 Bad 44
## 289 6.98 116 40 0 74 97 Medium 76
## 290 8.75 143 77 25 448 156 Medium 43
## 291 9.49 107 111 14 400 103 Medium 41
## 292 6.64 118 70 0 106 89 Bad 39
## 293 11.82 113 66 16 322 74 Good 76
## 294 11.28 123 84 0 74 89 Good 59
## 295 12.66 148 76 3 126 99 Good 60
## 296 4.21 118 35 14 502 137 Medium 79
## 297 8.21 127 44 13 160 123 Good 63
## 298 3.07 118 83 13 276 104 Bad 75
## 299 10.98 148 63 0 312 130 Good 63
## 300 9.40 135 40 17 497 96 Medium 54
## 301 8.57 116 78 1 158 99 Medium 45
## 302 7.41 99 93 0 198 87 Medium 57
## 303 5.28 108 77 13 388 110 Bad 74
## 304 10.01 133 52 16 290 99 Medium 43
## 305 11.93 123 98 12 408 134 Good 29
## 306 8.03 115 29 26 394 132 Medium 33
## 307 4.78 131 32 1 85 133 Medium 48
## 308 5.90 138 92 0 13 120 Bad 61
## 309 9.24 126 80 19 436 126 Medium 52
## 310 11.18 131 111 13 33 80 Bad 68
## 311 9.53 175 65 29 419 166 Medium 53
## 312 6.15 146 68 12 328 132 Bad 51
## 313 6.80 137 117 5 337 135 Bad 38
## 314 9.33 103 81 3 491 54 Medium 66
## 315 7.72 133 33 10 333 129 Good 71
## 316 6.39 131 21 8 220 171 Good 29
## 317 15.63 122 36 5 369 72 Good 35
## 318 6.41 142 30 0 472 136 Good 80
## 319 10.08 116 72 10 456 130 Good 41
## 320 6.97 127 45 19 459 129 Medium 57
## 321 5.86 136 70 12 171 152 Medium 44
## 322 7.52 123 39 5 499 98 Medium 34
## 323 9.16 140 50 10 300 139 Good 60
## 324 10.36 107 105 18 428 103 Medium 34
## 325 2.66 136 65 4 133 150 Bad 53
## 326 11.70 144 69 11 131 104 Medium 47
## 327 4.69 133 30 0 152 122 Medium 53
## 328 6.23 112 38 17 316 104 Medium 80
## 329 3.15 117 66 1 65 111 Bad 55
## 330 11.27 100 54 9 433 89 Good 45
## 331 4.99 122 59 0 501 112 Bad 32
## 332 10.10 135 63 15 213 134 Medium 32
## 333 5.74 106 33 20 354 104 Medium 61
## 334 5.87 136 60 7 303 147 Medium 41
## 335 7.63 93 117 9 489 83 Bad 42
## 336 6.18 120 70 15 464 110 Medium 72
## 337 5.17 138 35 6 60 143 Bad 28
## 338 8.61 130 38 0 283 102 Medium 80
## 339 5.97 112 24 0 164 101 Medium 45
## 340 11.54 134 44 4 219 126 Good 44
## 341 7.50 140 29 0 105 91 Bad 43
## 342 7.38 98 120 0 268 93 Medium 72
## 343 7.81 137 102 13 422 118 Medium 71
## 344 5.99 117 42 10 371 121 Bad 26
## 345 8.43 138 80 0 108 126 Good 70
## 346 4.81 121 68 0 279 149 Good 79
## 347 8.97 132 107 0 144 125 Medium 33
## 348 6.88 96 39 0 161 112 Good 27
## 349 12.57 132 102 20 459 107 Good 49
## 350 9.32 134 27 18 467 96 Medium 49
## 351 8.64 111 101 17 266 91 Medium 63
## 352 10.44 124 115 16 458 105 Medium 62
## 353 13.44 133 103 14 288 122 Good 61
## 354 9.45 107 67 12 430 92 Medium 35
## 355 5.30 133 31 1 80 145 Medium 42
## 356 7.02 130 100 0 306 146 Good 42
## 357 3.58 142 109 0 111 164 Good 72
## 358 13.36 103 73 3 276 72 Medium 34
## 359 4.17 123 96 10 71 118 Bad 69
## 360 3.13 130 62 11 396 130 Bad 66
## 361 8.77 118 86 7 265 114 Good 52
## 362 8.68 131 25 10 183 104 Medium 56
## 363 5.25 131 55 0 26 110 Bad 79
## 364 10.26 111 75 1 377 108 Good 25
## 365 10.50 122 21 16 488 131 Good 30
## 366 6.53 154 30 0 122 162 Medium 57
## 367 5.98 124 56 11 447 134 Medium 53
## 368 14.37 95 106 0 256 53 Good 52
## 369 10.71 109 22 10 348 79 Good 74
## 370 10.26 135 100 22 463 122 Medium 36
## 371 7.68 126 41 22 403 119 Bad 42
## 372 9.08 152 81 0 191 126 Medium 54
## 373 7.80 121 50 0 508 98 Medium 65
## 374 5.58 137 71 0 402 116 Medium 78
## 375 9.44 131 47 7 90 118 Medium 47
## 376 7.90 132 46 4 206 124 Medium 73
## 377 16.27 141 60 19 319 92 Good 44
## 378 6.81 132 61 0 263 125 Medium 41
## 379 6.11 133 88 3 105 119 Medium 79
## 380 5.81 125 111 0 404 107 Bad 54
## 381 9.64 106 64 10 17 89 Medium 68
## 382 3.90 124 65 21 496 151 Bad 77
## 383 4.95 121 28 19 315 121 Medium 66
## 384 9.35 98 117 0 76 68 Medium 63
## 385 12.85 123 37 15 348 112 Good 28
## 386 5.87 131 73 13 455 132 Medium 62
## 387 5.32 152 116 0 170 160 Medium 39
## 388 8.67 142 73 14 238 115 Medium 73
## 389 8.14 135 89 11 245 78 Bad 79
## 390 8.44 128 42 8 328 107 Medium 35
## 391 5.47 108 75 9 61 111 Medium 67
## 392 6.10 153 63 0 49 124 Bad 56
## 393 4.53 129 42 13 315 130 Bad 34
## 394 5.57 109 51 10 26 120 Medium 30
## 395 5.35 130 58 19 366 139 Bad 33
## 396 12.57 138 108 17 203 128 Good 33
## 397 6.14 139 23 3 37 120 Medium 55
## 398 7.41 162 26 12 368 159 Medium 40
## 399 5.94 100 79 7 284 95 Bad 50
## 400 9.71 134 37 0 27 120 Good 49
## Education Urban US
## 1 17 Yes Yes
## 2 10 Yes Yes
## 3 12 Yes Yes
## 4 14 Yes Yes
## 5 13 Yes No
## 6 16 No Yes
## 7 15 Yes No
## 8 10 Yes Yes
## 9 10 No No
## 10 17 No Yes
## 11 10 No Yes
## 12 13 Yes Yes
## 13 18 Yes No
## 14 18 Yes Yes
## 15 18 Yes Yes
## 16 18 No No
## 17 13 Yes No
## 18 10 Yes Yes
## 19 17 No Yes
## 20 12 Yes Yes
## 21 18 Yes Yes
## 22 18 No Yes
## 23 13 Yes No
## 24 10 Yes No
## 25 12 Yes Yes
## 26 11 No No
## 27 11 No Yes
## 28 17 Yes No
## 29 11 Yes Yes
## 30 17 Yes Yes
## 31 12 Yes No
## 32 18 Yes Yes
## 33 10 No Yes
## 34 16 Yes Yes
## 35 17 Yes Yes
## 36 17 No Yes
## 37 18 No No
## 38 10 Yes Yes
## 39 15 Yes No
## 40 10 No No
## 41 17 No No
## 42 16 Yes No
## 43 18 Yes No
## 44 13 Yes Yes
## 45 13 Yes Yes
## 46 12 Yes Yes
## 47 15 No Yes
## 48 16 Yes No
## 49 18 Yes No
## 50 17 Yes No
## 51 16 Yes Yes
## 52 16 Yes No
## 53 18 Yes Yes
## 54 17 Yes Yes
## 55 17 No Yes
## 56 18 Yes Yes
## 57 17 Yes No
## 58 11 Yes No
## 59 16 Yes Yes
## 60 13 Yes No
## 61 13 Yes Yes
## 62 13 No No
## 63 17 Yes Yes
## 64 13 Yes Yes
## 65 16 No Yes
## 66 13 No No
## 67 18 Yes No
## 68 16 Yes Yes
## 69 13 Yes Yes
## 70 12 Yes No
## 71 12 Yes Yes
## 72 17 No Yes
## 73 15 Yes No
## 74 11 No Yes
## 75 13 No Yes
## 76 16 No Yes
## 77 15 Yes Yes
## 78 18 No Yes
## 79 12 Yes Yes
## 80 13 Yes No
## 81 11 Yes Yes
## 82 13 Yes No
## 83 17 Yes Yes
## 84 11 Yes Yes
## 85 18 No No
## 86 13 No No
## 87 15 Yes No
## 88 16 No Yes
## 89 10 Yes Yes
## 90 16 No No
## 91 11 No No
## 92 15 Yes Yes
## 93 12 Yes No
## 94 17 Yes No
## 95 11 Yes Yes
## 96 13 Yes Yes
## 97 16 No Yes
## 98 16 Yes Yes
## 99 16 No Yes
## 100 16 No Yes
## 101 12 No Yes
## 102 18 Yes No
## 103 16 No No
## 104 17 Yes Yes
## 105 12 Yes No
## 106 11 Yes Yes
## 107 18 No No
## 108 12 Yes No
## 109 16 Yes No
## 110 17 No No
## 111 14 Yes Yes
## 112 14 Yes Yes
## 113 12 Yes Yes
## 114 12 Yes Yes
## 115 13 Yes Yes
## 116 13 Yes No
## 117 10 No No
## 118 12 Yes No
## 119 11 Yes Yes
## 120 12 Yes Yes
## 121 13 Yes Yes
## 122 10 Yes Yes
## 123 10 Yes Yes
## 124 15 No Yes
## 125 14 Yes No
## 126 15 No No
## 127 16 Yes Yes
## 128 14 Yes Yes
## 129 13 Yes Yes
## 130 10 No Yes
## 131 12 Yes Yes
## 132 16 Yes No
## 133 10 Yes Yes
## 134 12 Yes Yes
## 135 16 Yes No
## 136 18 No Yes
## 137 18 No No
## 138 11 Yes No
## 139 10 Yes Yes
## 140 13 No Yes
## 141 18 Yes Yes
## 142 15 Yes No
## 143 15 Yes No
## 144 17 Yes Yes
## 145 11 No No
## 146 17 Yes Yes
## 147 14 Yes No
## 148 16 No Yes
## 149 14 No Yes
## 150 11 Yes Yes
## 151 10 No Yes
## 152 17 No Yes
## 153 13 No No
## 154 17 No Yes
## 155 16 No Yes
## 156 16 Yes No
## 157 16 Yes No
## 158 13 No Yes
## 159 10 No Yes
## 160 18 No No
## 161 12 No No
## 162 12 No Yes
## 163 13 Yes No
## 164 17 No No
## 165 13 No Yes
## 166 15 Yes Yes
## 167 11 Yes Yes
## 168 13 Yes No
## 169 10 Yes No
## 170 18 Yes Yes
## 171 10 Yes Yes
## 172 15 Yes Yes
## 173 16 Yes Yes
## 174 18 Yes Yes
## 175 15 No No
## 176 12 Yes No
## 177 11 No Yes
## 178 17 Yes Yes
## 179 14 No Yes
## 180 18 Yes Yes
## 181 13 Yes Yes
## 182 11 Yes No
## 183 13 Yes No
## 184 18 Yes Yes
## 185 11 No Yes
## 186 10 Yes Yes
## 187 17 No No
## 188 17 Yes No
## 189 15 Yes No
## 190 15 No Yes
## 191 13 No Yes
## 192 14 Yes Yes
## 193 14 No No
## 194 10 Yes Yes
## 195 11 Yes Yes
## 196 11 Yes Yes
## 197 16 Yes Yes
## 198 16 Yes No
## 199 10 Yes Yes
## 200 14 Yes Yes
## 201 12 No No
## 202 18 Yes No
## 203 10 No Yes
## 204 14 Yes No
## 205 14 Yes No
## 206 12 Yes No
## 207 17 Yes Yes
## 208 10 No No
## 209 12 Yes No
## 210 11 No Yes
## 211 14 No Yes
## 212 15 Yes Yes
## 213 11 Yes Yes
## 214 10 Yes Yes
## 215 18 Yes Yes
## 216 11 Yes Yes
## 217 17 Yes No
## 218 14 No No
## 219 14 Yes Yes
## 220 17 Yes Yes
## 221 10 Yes Yes
## 222 11 Yes No
## 223 13 Yes Yes
## 224 14 Yes Yes
## 225 13 No No
## 226 14 Yes No
## 227 14 Yes No
## 228 16 Yes Yes
## 229 11 No Yes
## 230 18 No No
## 231 14 No No
## 232 11 No No
## 233 15 Yes Yes
## 234 14 No Yes
## 235 16 No Yes
## 236 17 Yes Yes
## 237 10 Yes Yes
## 238 10 Yes Yes
## 239 13 Yes No
## 240 16 Yes Yes
## 241 18 Yes No
## 242 12 Yes No
## 243 14 No No
## 244 10 Yes Yes
## 245 18 Yes No
## 246 10 No Yes
## 247 18 Yes Yes
## 248 16 Yes No
## 249 11 Yes Yes
## 250 11 Yes No
## 251 14 Yes Yes
## 252 13 Yes Yes
## 253 16 Yes No
## 254 12 No Yes
## 255 17 Yes Yes
## 256 15 Yes Yes
## 257 10 Yes No
## 258 13 Yes Yes
## 259 14 No No
## 260 11 No Yes
## 261 10 Yes Yes
## 262 15 Yes Yes
## 263 18 Yes Yes
## 264 17 Yes Yes
## 265 15 Yes Yes
## 266 17 Yes Yes
## 267 17 No Yes
## 268 12 No Yes
## 269 11 Yes No
## 270 17 Yes No
## 271 10 Yes No
## 272 16 Yes No
## 273 12 Yes No
## 274 12 Yes Yes
## 275 11 Yes Yes
## 276 11 Yes Yes
## 277 15 Yes Yes
## 278 16 Yes Yes
## 279 15 No Yes
## 280 18 Yes Yes
## 281 10 Yes Yes
## 282 16 No Yes
## 283 11 Yes No
## 284 16 No No
## 285 17 No No
## 286 10 Yes Yes
## 287 18 No Yes
## 288 17 Yes Yes
## 289 15 No No
## 290 17 Yes Yes
## 291 11 No Yes
## 292 17 Yes No
## 293 15 Yes Yes
## 294 10 Yes No
## 295 11 Yes Yes
## 296 10 No Yes
## 297 18 Yes Yes
## 298 10 Yes Yes
## 299 15 Yes No
## 300 17 No Yes
## 301 11 Yes Yes
## 302 16 Yes Yes
## 303 14 Yes Yes
## 304 11 Yes Yes
## 305 10 Yes Yes
## 306 13 Yes Yes
## 307 12 Yes Yes
## 308 12 Yes No
## 309 10 Yes Yes
## 310 18 Yes Yes
## 311 12 Yes Yes
## 312 14 Yes Yes
## 313 10 Yes Yes
## 314 13 Yes No
## 315 14 Yes Yes
## 316 14 Yes Yes
## 317 10 Yes Yes
## 318 15 No No
## 319 14 No Yes
## 320 11 No Yes
## 321 18 Yes Yes
## 322 15 Yes No
## 323 15 Yes Yes
## 324 12 Yes Yes
## 325 13 Yes Yes
## 326 11 Yes Yes
## 327 17 Yes No
## 328 16 Yes Yes
## 329 11 Yes Yes
## 330 12 Yes Yes
## 331 14 No No
## 332 10 Yes Yes
## 333 12 Yes Yes
## 334 10 Yes Yes
## 335 13 Yes Yes
## 336 15 Yes Yes
## 337 18 Yes No
## 338 15 Yes No
## 339 11 Yes No
## 340 15 Yes Yes
## 341 16 Yes No
## 342 10 No No
## 343 10 No Yes
## 344 14 Yes Yes
## 345 13 No Yes
## 346 12 Yes No
## 347 13 No No
## 348 14 No No
## 349 11 Yes Yes
## 350 14 No Yes
## 351 17 No Yes
## 352 16 No Yes
## 353 17 Yes Yes
## 354 12 No Yes
## 355 18 Yes Yes
## 356 11 Yes No
## 357 12 Yes No
## 358 15 Yes Yes
## 359 11 Yes Yes
## 360 14 Yes Yes
## 361 15 No Yes
## 362 15 No Yes
## 363 12 Yes Yes
## 364 12 Yes No
## 365 14 Yes Yes
## 366 17 No No
## 367 12 No Yes
## 368 17 Yes No
## 369 14 No Yes
## 370 14 Yes Yes
## 371 12 Yes Yes
## 372 16 Yes No
## 373 11 No No
## 374 17 Yes No
## 375 12 Yes Yes
## 376 11 Yes No
## 377 11 Yes Yes
## 378 12 No No
## 379 12 Yes Yes
## 380 15 Yes No
## 381 17 Yes Yes
## 382 13 Yes Yes
## 383 14 Yes Yes
## 384 10 Yes No
## 385 12 Yes Yes
## 386 17 Yes Yes
## 387 16 Yes No
## 388 14 No Yes
## 389 16 Yes Yes
## 390 12 Yes Yes
## 391 12 Yes Yes
## 392 16 Yes No
## 393 13 Yes Yes
## 394 17 No Yes
## 395 16 Yes Yes
## 396 14 Yes Yes
## 397 11 No Yes
## 398 18 Yes Yes
## 399 12 Yes Yes
## 400 16 Yes Yesattach(Carseats)Multiple regression model with interaction terms for Carseats dataset:
lm.fit.qual = lm(Sales ~ . + Income:Advertising + Price:Age, data = Carseats)
summary(lm.fit.qual)##
## Call:
## lm(formula = Sales ~ . + Income:Advertising + Price:Age, data = Carseats)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.9208 -0.7503 0.0177 0.6754 3.3413
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.5755654 1.0087470 6.519 2.22e-10 ***
## CompPrice 0.0929371 0.0041183 22.567 < 2e-16 ***
## Income 0.0108940 0.0026044 4.183 3.57e-05 ***
## Advertising 0.0702462 0.0226091 3.107 0.002030 **
## Population 0.0001592 0.0003679 0.433 0.665330
## Price -0.1008064 0.0074399 -13.549 < 2e-16 ***
## ShelveLocGood 4.8486762 0.1528378 31.724 < 2e-16 ***
## ShelveLocMedium 1.9532620 0.1257682 15.531 < 2e-16 ***
## Age -0.0579466 0.0159506 -3.633 0.000318 ***
## Education -0.0208525 0.0196131 -1.063 0.288361
## UrbanYes 0.1401597 0.1124019 1.247 0.213171
## USYes -0.1575571 0.1489234 -1.058 0.290729
## Income:Advertising 0.0007510 0.0002784 2.698 0.007290 **
## Price:Age 0.0001068 0.0001333 0.801 0.423812
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.011 on 386 degrees of freedom
## Multiple R-squared: 0.8761, Adjusted R-squared: 0.8719
## F-statistic: 210 on 13 and 386 DF, p-value: < 2.2e-16contrasts(ShelveLoc)## Good Medium
## Bad 0 0
## Good 1 0
## Medium 0 1========================EXERCISE========================
names(Auto)## [1] "mpg" "cylinders" "displacement" "horsepower"
## [5] "weight" "acceleration" "year" "origin"
## [9] "name"summary(Auto)## mpg cylinders displacement horsepower
## Min. : 9.00 Min. :3.000 Min. : 68.0 Min. : 46.0
## 1st Qu.:17.00 1st Qu.:4.000 1st Qu.:105.0 1st Qu.: 75.0
## Median :22.75 Median :4.000 Median :151.0 Median : 93.5
## Mean :23.45 Mean :5.472 Mean :194.4 Mean :104.5
## 3rd Qu.:29.00 3rd Qu.:8.000 3rd Qu.:275.8 3rd Qu.:126.0
## Max. :46.60 Max. :8.000 Max. :455.0 Max. :230.0
##
## weight acceleration year origin
## Min. :1613 Min. : 8.00 Min. :70.00 Min. :1.000
## 1st Qu.:2225 1st Qu.:13.78 1st Qu.:73.00 1st Qu.:1.000
## Median :2804 Median :15.50 Median :76.00 Median :1.000
## Mean :2978 Mean :15.54 Mean :75.98 Mean :1.577
## 3rd Qu.:3615 3rd Qu.:17.02 3rd Qu.:79.00 3rd Qu.:2.000
## Max. :5140 Max. :24.80 Max. :82.00 Max. :3.000
##
## name
## amc matador : 5
## ford pinto : 5
## toyota corolla : 5
## amc gremlin : 4
## amc hornet : 4
## chevrolet chevette: 4
## (Other) :365head(Auto, n=10)## mpg cylinders displacement horsepower weight acceleration year origin
## 1 18 8 307 130 3504 12.0 70 1
## 2 15 8 350 165 3693 11.5 70 1
## 3 18 8 318 150 3436 11.0 70 1
## 4 16 8 304 150 3433 12.0 70 1
## 5 17 8 302 140 3449 10.5 70 1
## 6 15 8 429 198 4341 10.0 70 1
## 7 14 8 454 220 4354 9.0 70 1
## 8 14 8 440 215 4312 8.5 70 1
## 9 14 8 455 225 4425 10.0 70 1
## 10 15 8 390 190 3850 8.5 70 1
## name
## 1 chevrolet chevelle malibu
## 2 buick skylark 320
## 3 plymouth satellite
## 4 amc rebel sst
## 5 ford torino
## 6 ford galaxie 500
## 7 chevrolet impala
## 8 plymouth fury iii
## 9 pontiac catalina
## 10 amc ambassador dplattach(Auto)lm.fit.auto = lm(mpg ~ horsepower, data = Auto)
summary(lm.fit.auto)##
## Call:
## lm(formula = mpg ~ horsepower, data = Auto)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.5710 -3.2592 -0.3435 2.7630 16.9240
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.935861 0.717499 55.66 <2e-16 ***
## horsepower -0.157845 0.006446 -24.49 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.906 on 390 degrees of freedom
## Multiple R-squared: 0.6059, Adjusted R-squared: 0.6049
## F-statistic: 599.7 on 1 and 390 DF, p-value: < 2.2e-16mean(mpg)## [1] 23.44592plot(horsepower, mpg)
abline(h=mean(mpg))
abline(lm.fit.auto, col = "blue")
plot(lm.fit.auto)
# prediction
predict(lm.fit.auto ,data.frame(horsepower=c(98)),interval ="confidence")## fit lwr upr
## 1 24.46708 23.97308 24.96108predict(lm.fit.auto ,data.frame(horsepower=c(98)),interval ="prediction")## fit lwr upr
## 1 24.46708 14.8094 34.12476ISLR: 3.9.
auto.without.name = Auto[1:8]
auto.without.name## mpg cylinders displacement horsepower weight acceleration year origin
## 1 18.0 8 307.0 130 3504 12.0 70 1
## 2 15.0 8 350.0 165 3693 11.5 70 1
## 3 18.0 8 318.0 150 3436 11.0 70 1
## 4 16.0 8 304.0 150 3433 12.0 70 1
## 5 17.0 8 302.0 140 3449 10.5 70 1
## 6 15.0 8 429.0 198 4341 10.0 70 1
## 7 14.0 8 454.0 220 4354 9.0 70 1
## 8 14.0 8 440.0 215 4312 8.5 70 1
## 9 14.0 8 455.0 225 4425 10.0 70 1
## 10 15.0 8 390.0 190 3850 8.5 70 1
## 11 15.0 8 383.0 170 3563 10.0 70 1
## 12 14.0 8 340.0 160 3609 8.0 70 1
## 13 15.0 8 400.0 150 3761 9.5 70 1
## 14 14.0 8 455.0 225 3086 10.0 70 1
## 15 24.0 4 113.0 95 2372 15.0 70 3
## 16 22.0 6 198.0 95 2833 15.5 70 1
## 17 18.0 6 199.0 97 2774 15.5 70 1
## 18 21.0 6 200.0 85 2587 16.0 70 1
## 19 27.0 4 97.0 88 2130 14.5 70 3
## 20 26.0 4 97.0 46 1835 20.5 70 2
## 21 25.0 4 110.0 87 2672 17.5 70 2
## 22 24.0 4 107.0 90 2430 14.5 70 2
## 23 25.0 4 104.0 95 2375 17.5 70 2
## 24 26.0 4 121.0 113 2234 12.5 70 2
## 25 21.0 6 199.0 90 2648 15.0 70 1
## 26 10.0 8 360.0 215 4615 14.0 70 1
## 27 10.0 8 307.0 200 4376 15.0 70 1
## 28 11.0 8 318.0 210 4382 13.5 70 1
## 29 9.0 8 304.0 193 4732 18.5 70 1
## 30 27.0 4 97.0 88 2130 14.5 71 3
## 31 28.0 4 140.0 90 2264 15.5 71 1
## 32 25.0 4 113.0 95 2228 14.0 71 3
## 34 19.0 6 232.0 100 2634 13.0 71 1
## 35 16.0 6 225.0 105 3439 15.5 71 1
## 36 17.0 6 250.0 100 3329 15.5 71 1
## 37 19.0 6 250.0 88 3302 15.5 71 1
## 38 18.0 6 232.0 100 3288 15.5 71 1
## 39 14.0 8 350.0 165 4209 12.0 71 1
## 40 14.0 8 400.0 175 4464 11.5 71 1
## 41 14.0 8 351.0 153 4154 13.5 71 1
## 42 14.0 8 318.0 150 4096 13.0 71 1
## 43 12.0 8 383.0 180 4955 11.5 71 1
## 44 13.0 8 400.0 170 4746 12.0 71 1
## 45 13.0 8 400.0 175 5140 12.0 71 1
## 46 18.0 6 258.0 110 2962 13.5 71 1
## 47 22.0 4 140.0 72 2408 19.0 71 1
## 48 19.0 6 250.0 100 3282 15.0 71 1
## 49 18.0 6 250.0 88 3139 14.5 71 1
## 50 23.0 4 122.0 86 2220 14.0 71 1
## 51 28.0 4 116.0 90 2123 14.0 71 2
## 52 30.0 4 79.0 70 2074 19.5 71 2
## 53 30.0 4 88.0 76 2065 14.5 71 2
## 54 31.0 4 71.0 65 1773 19.0 71 3
## 55 35.0 4 72.0 69 1613 18.0 71 3
## 56 27.0 4 97.0 60 1834 19.0 71 2
## 57 26.0 4 91.0 70 1955 20.5 71 1
## 58 24.0 4 113.0 95 2278 15.5 72 3
## 59 25.0 4 97.5 80 2126 17.0 72 1
## 60 23.0 4 97.0 54 2254 23.5 72 2
## 61 20.0 4 140.0 90 2408 19.5 72 1
## 62 21.0 4 122.0 86 2226 16.5 72 1
## 63 13.0 8 350.0 165 4274 12.0 72 1
## 64 14.0 8 400.0 175 4385 12.0 72 1
## 65 15.0 8 318.0 150 4135 13.5 72 1
## 66 14.0 8 351.0 153 4129 13.0 72 1
## 67 17.0 8 304.0 150 3672 11.5 72 1
## 68 11.0 8 429.0 208 4633 11.0 72 1
## 69 13.0 8 350.0 155 4502 13.5 72 1
## 70 12.0 8 350.0 160 4456 13.5 72 1
## 71 13.0 8 400.0 190 4422 12.5 72 1
## 72 19.0 3 70.0 97 2330 13.5 72 3
## 73 15.0 8 304.0 150 3892 12.5 72 1
## 74 13.0 8 307.0 130 4098 14.0 72 1
## 75 13.0 8 302.0 140 4294 16.0 72 1
## 76 14.0 8 318.0 150 4077 14.0 72 1
## 77 18.0 4 121.0 112 2933 14.5 72 2
## 78 22.0 4 121.0 76 2511 18.0 72 2
## 79 21.0 4 120.0 87 2979 19.5 72 2
## 80 26.0 4 96.0 69 2189 18.0 72 2
## 81 22.0 4 122.0 86 2395 16.0 72 1
## 82 28.0 4 97.0 92 2288 17.0 72 3
## 83 23.0 4 120.0 97 2506 14.5 72 3
## 84 28.0 4 98.0 80 2164 15.0 72 1
## 85 27.0 4 97.0 88 2100 16.5 72 3
## 86 13.0 8 350.0 175 4100 13.0 73 1
## 87 14.0 8 304.0 150 3672 11.5 73 1
## 88 13.0 8 350.0 145 3988 13.0 73 1
## 89 14.0 8 302.0 137 4042 14.5 73 1
## 90 15.0 8 318.0 150 3777 12.5 73 1
## 91 12.0 8 429.0 198 4952 11.5 73 1
## 92 13.0 8 400.0 150 4464 12.0 73 1
## 93 13.0 8 351.0 158 4363 13.0 73 1
## 94 14.0 8 318.0 150 4237 14.5 73 1
## 95 13.0 8 440.0 215 4735 11.0 73 1
## 96 12.0 8 455.0 225 4951 11.0 73 1
## 97 13.0 8 360.0 175 3821 11.0 73 1
## 98 18.0 6 225.0 105 3121 16.5 73 1
## 99 16.0 6 250.0 100 3278 18.0 73 1
## 100 18.0 6 232.0 100 2945 16.0 73 1
## 101 18.0 6 250.0 88 3021 16.5 73 1
## 102 23.0 6 198.0 95 2904 16.0 73 1
## 103 26.0 4 97.0 46 1950 21.0 73 2
## 104 11.0 8 400.0 150 4997 14.0 73 1
## 105 12.0 8 400.0 167 4906 12.5 73 1
## 106 13.0 8 360.0 170 4654 13.0 73 1
## 107 12.0 8 350.0 180 4499 12.5 73 1
## 108 18.0 6 232.0 100 2789 15.0 73 1
## 109 20.0 4 97.0 88 2279 19.0 73 3
## 110 21.0 4 140.0 72 2401 19.5 73 1
## 111 22.0 4 108.0 94 2379 16.5 73 3
## 112 18.0 3 70.0 90 2124 13.5 73 3
## 113 19.0 4 122.0 85 2310 18.5 73 1
## 114 21.0 6 155.0 107 2472 14.0 73 1
## 115 26.0 4 98.0 90 2265 15.5 73 2
## 116 15.0 8 350.0 145 4082 13.0 73 1
## 117 16.0 8 400.0 230 4278 9.5 73 1
## 118 29.0 4 68.0 49 1867 19.5 73 2
## 119 24.0 4 116.0 75 2158 15.5 73 2
## 120 20.0 4 114.0 91 2582 14.0 73 2
## 121 19.0 4 121.0 112 2868 15.5 73 2
## 122 15.0 8 318.0 150 3399 11.0 73 1
## 123 24.0 4 121.0 110 2660 14.0 73 2
## 124 20.0 6 156.0 122 2807 13.5 73 3
## 125 11.0 8 350.0 180 3664 11.0 73 1
## 126 20.0 6 198.0 95 3102 16.5 74 1
## 128 19.0 6 232.0 100 2901 16.0 74 1
## 129 15.0 6 250.0 100 3336 17.0 74 1
## 130 31.0 4 79.0 67 1950 19.0 74 3
## 131 26.0 4 122.0 80 2451 16.5 74 1
## 132 32.0 4 71.0 65 1836 21.0 74 3
## 133 25.0 4 140.0 75 2542 17.0 74 1
## 134 16.0 6 250.0 100 3781 17.0 74 1
## 135 16.0 6 258.0 110 3632 18.0 74 1
## 136 18.0 6 225.0 105 3613 16.5 74 1
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## 387 38.0 6 262.0 85 3015 17.0 82 1
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## 391 36.0 4 135.0 84 2370 13.0 82 1
## 392 27.0 4 151.0 90 2950 17.3 82 1
## 393 27.0 4 140.0 86 2790 15.6 82 1
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## 396 28.0 4 120.0 79 2625 18.6 82 1
## 397 31.0 4 119.0 82 2720 19.4 82 1cor(auto.without.name)## mpg cylinders displacement horsepower weight
## mpg 1.0000000 -0.7776175 -0.8051269 -0.7784268 -0.8322442
## cylinders -0.7776175 1.0000000 0.9508233 0.8429834 0.8975273
## displacement -0.8051269 0.9508233 1.0000000 0.8972570 0.9329944
## horsepower -0.7784268 0.8429834 0.8972570 1.0000000 0.8645377
## weight -0.8322442 0.8975273 0.9329944 0.8645377 1.0000000
## acceleration 0.4233285 -0.5046834 -0.5438005 -0.6891955 -0.4168392
## year 0.5805410 -0.3456474 -0.3698552 -0.4163615 -0.3091199
## origin 0.5652088 -0.5689316 -0.6145351 -0.4551715 -0.5850054
## acceleration year origin
## mpg 0.4233285 0.5805410 0.5652088
## cylinders -0.5046834 -0.3456474 -0.5689316
## displacement -0.5438005 -0.3698552 -0.6145351
## horsepower -0.6891955 -0.4163615 -0.4551715
## weight -0.4168392 -0.3091199 -0.5850054
## acceleration 1.0000000 0.2903161 0.2127458
## year 0.2903161 1.0000000 0.1815277
## origin 0.2127458 0.1815277 1.0000000#as.data.frame(as.table(cor(auto.without.name)))lm.fit.auto.mul = lm(mpg ~ ., data = auto.without.name)
summary(lm.fit.auto.mul)##
## Call:
## lm(formula = mpg ~ ., data = auto.without.name)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.5903 -2.1565 -0.1169 1.8690 13.0604
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -17.218435 4.644294 -3.707 0.00024 ***
## cylinders -0.493376 0.323282 -1.526 0.12780
## displacement 0.019896 0.007515 2.647 0.00844 **
## horsepower -0.016951 0.013787 -1.230 0.21963
## weight -0.006474 0.000652 -9.929 < 2e-16 ***
## acceleration 0.080576 0.098845 0.815 0.41548
## year 0.750773 0.050973 14.729 < 2e-16 ***
## origin 1.426141 0.278136 5.127 4.67e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.328 on 384 degrees of freedom
## Multiple R-squared: 0.8215, Adjusted R-squared: 0.8182
## F-statistic: 252.4 on 7 and 384 DF, p-value: < 2.2e-16plot(lm.fit.auto.mul)
lm.fit.auto.mul1 = lm(mpg ~ displacement*cylinders + displacement * weight, data = auto.without.name)
summary(lm.fit.auto.mul1)##
## Call:
## lm(formula = mpg ~ displacement * cylinders + displacement *
## weight, data = auto.without.name)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.2934 -2.5184 -0.3476 1.8399 17.7723
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.262e+01 2.237e+00 23.519 < 2e-16 ***
## displacement -7.351e-02 1.669e-02 -4.403 1.38e-05 ***
## cylinders 7.606e-01 7.669e-01 0.992 0.322
## weight -9.888e-03 1.329e-03 -7.438 6.69e-13 ***
## displacement:cylinders -2.986e-03 3.426e-03 -0.872 0.384
## displacement:weight 2.128e-05 5.002e-06 4.254 2.64e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.103 on 386 degrees of freedom
## Multiple R-squared: 0.7272, Adjusted R-squared: 0.7237
## F-statistic: 205.8 on 5 and 386 DF, p-value: < 2.2e-16plot(lm.fit.auto.mul1)
From the above result, we can see that cylinders and the interaction displacement*cylinders are not significant.
lm.fit.auto.mul2 = lm(mpg ~ displacement + weight + displacement:weight, data = auto.without.name)
summary(lm.fit.auto.mul2)##
## Call:
## lm(formula = mpg ~ displacement + weight + displacement:weight,
## data = auto.without.name)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.8664 -2.4801 -0.3355 1.8071 17.9429
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.372e+01 1.940e+00 27.697 < 2e-16 ***
## displacement -7.831e-02 1.131e-02 -6.922 1.85e-11 ***
## weight -8.931e-03 8.474e-04 -10.539 < 2e-16 ***
## displacement:weight 1.744e-05 2.789e-06 6.253 1.06e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.097 on 388 degrees of freedom
## Multiple R-squared: 0.7265, Adjusted R-squared: 0.7244
## F-statistic: 343.6 on 3 and 388 DF, p-value: < 2.2e-16plot(lm.fit.auto.mul2)
